A magnetic 2-monopole is a soliton solution of charge 2 of Bogomolny equations in the Yang–Mills–Higgs theory in \(\mathbb {R}^3\) , where \({\rm SU}(2)\)  Yang–Mills is a gauge theory of 1-form connections \(\bf {A}\)  on a principal \({\rm SU}(2)\) -bundle while the Higgs field \(\Phi \)  correspond to a section of an associated \(\mathfrak {su}(2)\) -bundle [1]}, [2]}. In [1]}, Atiyah and Hitchin showed that the reduced moduli \(M^0_2\)  of 2-monopoles is a 4-dimensional hyperkähler manifold and an anti-self-dual (curvature-wise) Einstein manifold. Since \(M^0_2\)  admits \({\rm SO}(3)\)  isometry, the metric is a Bianch IXNote that here the four coordinates of the moduli are not spacetime directions, but internal parameters of a 2-monopole solution. (REF ). This is a consequence of the hyperkähler structure of \(M^0_2\)  which has an \(S^2\) -parameter family of complex structures, i.e., if \(I\) , \(J\) , \(K\)  are covariantly constant complex structures in \(M^0_2\)  then \(aI+bJ+cK\)  is also a covariantly
constant complex structure in \(M^0_2\)  given that \(a^2+b^2+c^2=1\) .
